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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On the reflexivity of multivariable isometries


Author: Jörg Eschmeier
Journal: Proc. Amer. Math. Soc. 134 (2006), 1783-1789
MSC (2000): Primary 47A15; Secondary 47A13, 47B20, 47L45
Published electronically: December 15, 2005
MathSciNet review: 2207494
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Abstract: Let $ A \subset C(K)$ be a unital closed subalgebra of the algebra of all continuous functions on a compact set $ K$ in $ \mathbb{C}^n$. We define the notion of an $ A$-isometry and show that, under a suitable regularity condition needed to apply Aleksandrov's work on the inner function problem, every $ A$-isometry $ T \in L(\mathcal H)^n$ is reflexive. This result applies to commuting isometries, spherical isometries, and more generally, to all subnormal tuples with normal spectrum contained in the Bergman-Shilov boundary of a strictly pseudoconvex or bounded symmetric domain.


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Additional Information

Jörg Eschmeier
Affiliation: Fachrichtung Mathematik, Universität des Saarlandes, Postfach 151150, D–66041 Saarbrücken, Germany
Email: eschmei@math.uni-sb.de

DOI: http://dx.doi.org/10.1090/S0002-9939-05-08139-6
PII: S 0002-9939(05)08139-6
Received by editor(s): January 14, 2005
Received by editor(s) in revised form: January 31, 2005
Published electronically: December 15, 2005
Communicated by: Joseph A. Ball
Article copyright: © Copyright 2005 American Mathematical Society